Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
From inside the book
Results 1-5 of 26
Page 27
... extremities of any side , their sum will be less than that of the two remaining sides of the triangle . A Let be any point within the triangle BAC , and let the lines OB , OC , be drawn to the extremities of any side , as BC : then will ...
... extremities of any side , their sum will be less than that of the two remaining sides of the triangle . A Let be any point within the triangle BAC , and let the lines OB , OC , be drawn to the extremities of any side , as BC : then will ...
Page 35
... extremities of the line : 2o . Any point , without the perpendicular , will be unequally distant from the extremities . " Let AB be a given straight line , C its middle point , and EF the perpendicular . Then will any point of EF be ...
... extremities of the line : 2o . Any point , without the perpendicular , will be unequally distant from the extremities . " Let AB be a given straight line , C its middle point , and EF the perpendicular . Then will any point of EF be ...
Page 59
... extremities of an arc . Any chord belongs to two arcs : the smaller one is meant , unless the contrary is expressed . 6. A SEGMENT is a part of a circle included between an arc and its chord . 7. A SECTOR is a part of a circle included ...
... extremities of an arc . Any chord belongs to two arcs : the smaller one is meant , unless the contrary is expressed . 6. A SEGMENT is a part of a circle included between an arc and its chord . 7. A SECTOR is a part of a circle included ...
Page 61
... extremity , as A : then will AB be greater than AD . Draw the radius CD . In the tri- angle ACD , we have AD less than the sum of AC and CD ( B. I. , P. VII . ) . But this sum is equal to AB ( D. 3 ) : hence , AB is greater than AD ...
... extremity , as A : then will AB be greater than AD . Draw the radius CD . In the tri- angle ACD , we have AD less than the sum of AC and CD ( B. I. , P. VII . ) . But this sum is equal to AB ( D. 3 ) : hence , AB is greater than AD ...
Page 68
... extremity , it will be tangent to the circle at that point ; conversely , if a straight line is tangent to a circle at any point , it will be perpendicular to the radius drawn to that point . 1o . Let BD be perpendicular to the radius ...
... extremity , it will be tangent to the circle at that point ; conversely , if a straight line is tangent to a circle at any point , it will be perpendicular to the radius drawn to that point . 1o . Let BD be perpendicular to the radius ...
Other editions - View all
Common terms and phrases
AB² AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence